Mr. stokes, 0\ THE VARIATION OF GRAVITY, ETC. 673 



the observed ellipticity and that calculated with an assumed law of density which is likely a priori 

 to be not far from the truth, and which is confirmed, as to its general correctness, by leading to a 

 value for the annual precession which does not much differ from the observed value. 



Since the earth's actual surface is not strictly a surface of equilibrium, on account of the ele- 

 vation of the continents and islands above the sea level, it is necessary to consider in the first 

 instance in what manner observations would have to be reduced in order to render the preceding 

 theory applicable. It is shewn in Art. 13 that the earth may be regarded as bounded by a surface 

 of equilibrium, and therefore the expressions previously investigated may be applied, provided the 

 sea level be regarded as the bounding surface, and observed gravity be reduced to the level of the 

 sea by taking account only of the change of distance from the earth's centre. Gravity reduced in 

 this manner would, however, be liable to vary irregularly from one place to another, in consequence 

 of the attraction of the land between the station and the surface of the sea, supposed to be prolono-ed 

 underground, since this attraction would be greater or less according to the height of the station 

 above the sea level. In order therefore to render the observations taken at different places com- 

 parable with one another, it seems best to correct for this attraction in reducing to the level of the 

 sea ; but since this additional correction is introduced in violation of the theory in which the earth's 

 surface is regarded as one of equilibrium, it is necessary to consider what effect the habitual neo-Iect 

 of the small attraction above mentioned produces on the values of mean gravity and of the ellipticity 

 deduced from observations taken at a number of stations. These effects are considered in Arts. 

 17, 18. 



Besides the consideration of the mode of determining the values of mean gravity, and 

 thereby the mass of the earth, and of the ellipticity, and thereby the effect of the earth's 

 oblateness on the motion of the moon, it is an interesting question to consider whether the 

 observed anomalies in the variation of gravity may be attributed wholly or mainly to the 

 irregular distribution of land and sea at the surface of the earth, or whether they must be 

 referred to more deeply seated causes. In Arts. 19, 20, I have considered the effect of the excess of 

 matter in islands and continents, consisting of the matter which is there situated above the actual 

 sea level, and of the defect of matter in the sea, consisting of the difference between the mass 

 of the sea, and the mass of an equal bulk of rock or clay. It appears that besides the attrac- 

 tion of the land lying immediately underneath a continental station, between it and the level of 

 the sea, the more distant portions of the continent cause an increase in gravity, since the attraction 

 which they exert is not wholly horizontal, on account of the curvature of the earth. But besides 

 this direct effect, a continent produces an indirect effect on the magnitude of apparent gravity. 

 For the horizontal attraction causes the verticals to point more inwards, that is, the zeniths to 

 be situated further outwards, than if the continent did not exist; and since a level surface is 

 everywhere perpendicular to the vertical, it follows that the sea level on a continent is higher than 

 it would be at the same place if the continent did not exist. Hence, in reducing an observation 

 taken at a continental station to the level of the sea, we reduce it to a point more distant from 

 the centre of the earth than if the continent were away ; and therefore, on this account alone, 

 gravity is less on a continent than on an island. It appears tiiat this latter effect more than 

 counterbalances the former, so that on the whole, gravity is less on a continent than on an island, 

 especially if the island be situated in the middle of an ocean. This circumstance lias already 

 been noticed as tiie result of ol)scrvati<)n. In consequence of the iiicciuaiity to which gravity is 

 subject, de])ending on the cliaracter of the station, it is pr()l);il)le that tiie value of tile ellipticity 

 which Mr. Airv has deduced from his discussion of pendulum observations is a little too great, on 

 account of the decided preponderance of oceanic stations in low latitudes among the group of 

 stations where the observations were taken. 



The alteration of attraction produced by the excess anil defect of matter mentioned in tiie 



